Whakaoti i te x^2-5000002x+10

$${ x }^{ 2 } -5000002x+10$$

Tauwehe

$$\left(x-\left(2500001-3\sqrt{694444999999}\right)\right)\left(x-\left(3\sqrt{694444999999}+2500001\right)\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$x^{2}-5000002x+10=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$x=\frac{-\left(-5000002\right)±\sqrt{\left(-5000002\right)^{2}-4\times 10}}{2}$$

Pūrua -5000002.

$$x=\frac{-\left(-5000002\right)±\sqrt{25000020000004-4\times 10}}{2}$$

Whakareatia -4 ki te 10.

$$x=\frac{-\left(-5000002\right)±\sqrt{25000020000004-40}}{2}$$

Tāpiri 25000020000004 ki te -40.

$$x=\frac{-\left(-5000002\right)±\sqrt{25000019999964}}{2}$$

Tuhia te pūtakerua o te 25000019999964.

$$x=\frac{-\left(-5000002\right)±6\sqrt{694444999999}}{2}$$

Ko te tauaro o -5000002 ko 5000002.

$$x=\frac{5000002±6\sqrt{694444999999}}{2}$$

Nā, me whakaoti te whārite x=\frac{5000002±6\sqrt{694444999999}}{2} ina he tāpiri te ±. Tāpiri 5000002 ki te 6\sqrt{694444999999}.

$$x=\frac{6\sqrt{694444999999}+5000002}{2}$$

Whakawehe 5000002+6\sqrt{694444999999} ki te 2.

$$x=3\sqrt{694444999999}+2500001$$

Nā, me whakaoti te whārite x=\frac{5000002±6\sqrt{694444999999}}{2} ina he tango te ±. Tango 6\sqrt{694444999999} mai i 5000002.

$$x=\frac{5000002-6\sqrt{694444999999}}{2}$$

Whakawehe 5000002-6\sqrt{694444999999} ki te 2.

$$x=2500001-3\sqrt{694444999999}$$

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te 2500001+3\sqrt{694444999999} mō te x_{1} me te 2500001-3\sqrt{694444999999} mō te x_{2}.

$$x^{2}-5000002x+10=\left(x-\left(3\sqrt{694444999999}+2500001\right)\right)\left(x-\left(2500001-3\sqrt{694444999999}\right)\right)$$

Aromātai

$$x^{2}-5000002x+10$$